The compactness conjecture for type spaces of finitely forcible graphons

Let ${\cal W}_0$ be the space of graphons under consideration, and let $T(W)$ denote the type space associated with a graphon $W$. Compactness conjecture. If $W$ is finitely forcible in ${\cal W}_0$, then $T(W)$ is a compact space. The source notes that even local compactness of $T(W)$ is not known in general. This conjecture concerns the topology of type spaces arising from finitely forcible graphons, which are compact in all examples discussed in the paper.